In order to understand these recently observed charmonium-like states, a better understanding of
the charmonium spectrum can be regarded as a prerequisite. In this work we take the strategy of
studying systematically the charmonium open flavor decays within the widely used
linear potential (LP) model [1]}, [2]}, [3]} and
screened potential (SP) model [4]}, [5]} such that most of the conventional
charmonium states can be identified by comparing with the experimental measurements. Although it
should be recognized that the SP model may not be sufficient for including the full open threshold effects,
we anticipate that unusual phenomena arising from such a study would indicate signals for unconventional
structures of some of those charmonium-like states. In Ref. [6]} the charmonium spectrum
and their electromagnetic (EM) transitions have been studied within both LP and SP models.
For the low-lying charmonium states with a mass of \(M<4.0\)  GeV, both models give comparable predictions.
However, for the higher charmonium states with a mass of \(M>4.1\)  GeV,
the SP model gives very different results from the LP model.
For example, in the SP model, the \(J^{PC}=1^{--}\)  charmonium-like states \(Y(4260)\)  and \(Y(4360)\) 
are good candidates for the \(\psi (4S)\)  and \(\psi _1(3D)\)  states, respectively,
while the \(J^{PC}=1^{++}\)  charmonium-like states \(X(4140)\)  may be
assigned as the \(\chi _{c1}(3P)\)  state. In contrast, there is no
room for the charmonium-like states \(Y(4260)\) , \(Y(4360)\)  and \(X(4140)\) 
in the LP model, the well-established state \(\psi (4415)\)  may be
assigned to \(\psi (4S)\)  or \(\psi _1(3D)\) , and the charmonium-like states \(X(4274)\) 
seems to be a candidate of \(\chi _{c1}(3P)\) . Such a result has already shown different dynamic origins introduced by the color screening effects. To clarify the nature of the newly observed charmonium-like states, we continue to investigate the open-flavor strong decays in the SP and LP models in this work. The differences between these two models and their comparisons with experimental observations can provide valuable information on the internal structures of these charmonium-like states.
